Paper Citation Record · LEDGER

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks

As of 10 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2606.02078.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2606.02078 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-28T15:34:55.812512Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

36 of 36 outbound references displayed

verified exact1
verified fuzzy0
unresolved34
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 342c4886-a833-4edf-9c27-cb4d5b9f48d0 · outbound

This paper cites Neural Networks 197: 108481 (2026).

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Neural Networks 197: 108481 (2026)

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f85ae881-db09-47b1-a7fc-13bb4e30e52c · outbound

This paper cites Neural Networks 197: 108453 (2026).

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Neural Networks 197: 108453 (2026)

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 254de364-33bc-4a10-a57d-5d5c21e5b612 · outbound

This paper cites Neural Networks 196: 108388 (2026).

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Neural Networks 196: 108388 (2026)

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation deb651af-79f9-416b-a4b2-a84f4295f683 · outbound

This paper cites A stochastic approximation method[J].

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks A stochastic approximation method[J]

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0175fffc-6832-4b6a-b686-fda4b9c9d7f0 · outbound

This paper cites Learning from streaming video with orthogonal gradients[C]//Proceedings of the Computer Vision and Pat- tern Recognition Conference.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Learning from streaming video with orthogonal gradients[C]//Proceedings of the Computer Vision and Pat- tern Recognition Conference

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0b71dbf-130f-4be2-b38a-62f915da5fe0 · outbound

This paper cites Resolving discrepancies in compute-optimal scaling of language models[J].

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Resolving discrepancies in compute-optimal scaling of language models[J]

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3302cc07-8caa-41f0-88b9-6e8800803a1d · outbound

This paper cites Kingma, Jimmy Ba: Adam: A Method for Stochastic Opti- mization.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Kingma, Jimmy Ba: Adam: A Method for Stochastic Opti- mization

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5c66ee3-5a2e-49d8-b34c-8dce9b856cbd · outbound

This paper cites ICLR (Poster) 2019.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks ICLR (Poster) 2019

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc209f34-e2d9-4c39-87ab-9c054cbf2a81 · outbound

This paper cites Adaptive subgradient methods for online learning and stochastic optimization[J].

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Adaptive subgradient methods for online learning and stochastic optimization[J]

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c4136512-2f5d-4425-9ed5-e12ef4f6e482 · outbound

This paper cites RMSprop converges with proper hyper- parameter[C]//International Conference on Learning Representations.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks RMSprop converges with proper hyper- parameter[C]//International Conference on Learning Representations

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 957ae3ab-4180-4345-94ff-d30afab10f9d · outbound

This paper cites The Geometry of Sign Gradient Descent.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks The Geometry of Sign Gradient Descent

Reference 11

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T22:16:16.321542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2c694ffa-f1a5-4e11-af89-a3f36fdd2dc3 · outbound

This paper cites signSGD: Compressed optimisation for non-convex problems[C]//International conference on machine learning.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks signSGD: Compressed optimisation for non-convex problems[C]//International conference on machine learning

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1c22cfd-7d3d-4e0d-a02e-2e8eb30028df · outbound

This paper cites Le: Symbolic Discovery of Optimization Algorithms.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Le: Symbolic Discovery of Optimization Algorithms

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 230bff13-897f-4391-937c-30eed87c0af4 · outbound

This paper cites ICLR 2024.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks ICLR 2024

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc1eb39c-43a9-4eab-9625-d875f9f4b7bd · outbound

This paper cites Dissecting adam: The sign, magnitude and vari- ance of stochastic gradients[C]//International Conference on Machine Learning.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Dissecting adam: The sign, magnitude and vari- ance of stochastic gradients[C]//International Conference on Machine Learning

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0a82ae2-8fa1-4a89-8f0f-97db9ac494f8 · outbound

This paper cites Equilibrated adaptive learning rates for non-convex optimization[J].

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Equilibrated adaptive learning rates for non-convex optimization[J]

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c19ba9c-3164-4436-b033-7ad22af5dac4 · outbound

This paper cites Zico Kolter, Ameet Tal- walkar: Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Zico Kolter, Ameet Tal- walkar: Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acc87a9c-6d61-4409-8652-b00ad32e40c7 · outbound

This paper cites On faster convergence of scaled sign gradient descent[J].

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks On faster convergence of scaled sign gradient descent[J]

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d5922591-477b-4ca5-a88e-bfb830f04e2f · outbound

This paper cites Deep resid- uallearningforimage recognition.In Proceedingsof the2016 IEEECon- ference on Computer Vision and Pattern Recognition, pages 770–778, Las Vegas, NV, USA, June 2016.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Deep resid- uallearningforimage recognition.In Proceedingsof the2016 IEEECon- ference on Computer Vision and Pattern Recognition, pages 770–778, Las Vegas, NV, USA, June 2016

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bf31eade-3b1a-4bb0-8324-85e1ad205104 · outbound

This paper cites Learning multiple layers of features from tiny images.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Learning multiple layers of features from tiny images

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee5cf22e-bdf4-49f4-a8a9-2830cdf4d7d4 · outbound

This paper cites Ugur Güney, Yann N.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Ugur Güney, Yann N

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5395edf8-2311-489f-9c1b-feeb68e45328 · outbound

This paper cites Geometry of neural network loss surfaces via random matrix theory[C]//International conference on machine learn- ing.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Geometry of neural network loss surfaces via random matrix theory[C]//International conference on machine learn- ing

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 40bf213a-c639-40f4-93d7-7b3fdf8ef6d0 · outbound

This paper cites An investigation into neural net op- timization via hessian eigenvalue density[C]//International Conference on Machine Learning.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks An investigation into neural net op- timization via hessian eigenvalue density[C]//International Conference on Machine Learning

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c980db6f-cc91-45da-af5c-38e25614572c · outbound

This paper cites Pyhessian: Neural networks through the lens of the hessian[C]//2020 IEEE international conference on big data (Big data).

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Pyhessian: Neural networks through the lens of the hessian[C]//2020 IEEE international conference on big data (Big data)

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28ec0ef8-21ee-4279-81e8-59231ed6aa0e · outbound

This paper cites A deeper look at the hessian eigenspectrum of deep neural networks and its applications to regularization[C]//Proceedings of the AAAI Conference on Artificial In- telligence.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks A deeper look at the hessian eigenspectrum of deep neural networks and its applications to regularization[C]//Proceedings of the AAAI Conference on Artificial In- telligence

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30d73556-085d-4b65-b2ee-2c2d3a26c848 · outbound

This paper cites Optimizing neural networks with kronecker- factored approximate curvature[C]//International conference on ma- chine learning.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Optimizing neural networks with kronecker- factored approximate curvature[C]//International conference on ma- chine learning

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d59908f-9e02-425b-985c-5181905223a6 · outbound

This paper cites Shampoo: Preconditioned stochastic tensor optimization[C]//International Conference on Machine Learning.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Shampoo: Preconditioned stochastic tensor optimization[C]//International Conference on Machine Learning

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14ae73e8-68b7-4a5a-b812-a3e4647bf97c · outbound

This paper cites ICLR 2024.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks ICLR 2024

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d09554a-eaee-4664-a527-b70343a61c8e · outbound

This paper cites Sharpness-aware lookahead for accelerat- ing convergence and improving generalization[J].

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Sharpness-aware lookahead for accelerat- ing convergence and improving generalization[J]

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0fa9d557-3fa9-4c52-980f-3410b0df5154 · outbound

This paper cites ICML 2025.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks ICML 2025

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b781c704-3a1c-4c09-8e96-874a59e62a16 · outbound

This paper cites Gradual Stochastic Gradient Descent: from signSGD to SGD viaℓp Norm[C]//Workshop on Scientific Methods for Understanding Deep Learning.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Gradual Stochastic Gradient Descent: from signSGD to SGD viaℓp Norm[C]//Workshop on Scientific Methods for Understanding Deep Learning

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 365469ac-340d-4074-b2d4-19a6d00b1226 · outbound

This paper cites Continual momentum filtering on parameter space for online test-time adaptation[C]//The twelfth international conference on learning representations.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Continual momentum filtering on parameter space for online test-time adaptation[C]//The twelfth international conference on learning representations

Reference 33

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2679c045-e137-4c56-9114-604dfe433ada · outbound

This paper cites Adaptive momentum-based optimization to train deep neural network for simulating the static sta- bility of the composite structure[J].

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Adaptive momentum-based optimization to train deep neural network for simulating the static sta- bility of the composite structure[J]

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 446e295e-8f3e-4657-bc40-2bb52547e017 · outbound

This paper cites 1983, 269: 543.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks 1983, 269: 543

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4e3d3cc6-0a91-4a90-a90f-851d9e4e0384 · outbound

This paper cites Very Deep Convolutional Networks for Large-Scale Image Recognition.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Very Deep Convolutional Networks for Large-Scale Image Recognition

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-07-01T22:16:16.324406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation cac39745-734e-413b-9eff-81c7ec1ce67a · outbound

This paper cites Ima- genet: A large-scale hierarchical image database.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks Ima- genet: A large-scale hierarchical image database

Reference 37

Resolution: unresolved; no resolver link, observed 2026-06-28T15:34:55.812512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.